Why am I getting billed for purchases on itunes and app store when on a family plan?

Are the Organizer of your Family Sharing account, and your card is the Shared Payment Method? If so that could be it. Look in settings/iCloud/Family. It will list everyone on the account, who is the Organizer, and the shared payment method. If the family members have money in their iTunes account, it will funds from there first.

As JML5150 stated, you should check to see if you are in fact the Organizer. Whatever payment method is listed by you will be used for purchases made by any of the family members you have listed under Family Sharing.
Please see the link for more info and clarification.